Polynomial equations with one catalytic variable, algebraic series, and map enumeration
| dc.creator | Bousquet-Mélou, Mireille | |
| dc.creator | Jehanne, Arnaud | |
| dc.date | 2005-04-01 | |
| dc.date.accessioned | 2026-07-07T09:36:46Z | |
| dc.date.available | 2026-07-07T09:36:46Z | |
| dc.description | Let $F(t,u)\equiv F(u)$ be a formal power series in $t$ with polynomial coefficients in $u$. Let $F\_1, ..., F\_k$ be $k$ formal power series in $t$, independent of $u$. Assume all these series are characterized by a polynomial equation $$ P(F(u), F\_1, ..., F\_k, t, u)=0. $$ We prove that, under a mild hypothesis on the form of this equation, these $(k+1)$ series are algebraic, and we give a strategy to compute a polynomial equation for each of them. This strategy generalizes the so-called kernel method, and quadratic method, which apply respectively to equations that are linear and quadratic in $F(u)$. Applications include the solution of numerous map enumeration problems, among which the hard-particle model on general planar maps. | |
| dc.identifier | https://arxiv.org/abs/math/0504018 | |
| dc.identifier | http://arxiv.org/abs/math/0504018 | |
| dc.identifier | Journal of Combinatorial Theory Series B 96 (2006) 623--672 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160232 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Polynomial equations with one catalytic variable, algebraic series, and map enumeration | |
| dc.type | text |